Nonextensive Statistical Mechanics

230 7 Thermodynamical and Nonthermodynamical ApplicationsFig. 7.9 Time evolution of the second moments of position trajectories in x and y. Solid line is thediffusive behavior predicted by Eq. (4.16) with q = 3/2, i.e., α = 4/3; dotted line corresponds tonormal diffusion (q = 1). Fits to the data give values of α in the range 1.16–1.5, depending on theregion being fit (from [427]).7.1.3.3 Couette–Taylor FlowLagrangian and Eulerian experiments have been done of fluid motion within tworotating concentric cylinders, and results for the velocity distributions have beencompared with q-Gaussians. A large literature exists on the subject, but here we onlyprovide a few typical illustrations [328]: see Fig. 7.10. Further details on Eulerianexperiments are indicated in Figs. 7.11 and 7.12. Data collapse for the values ofq is possible: see Fig. 7.13. Recent developments suggest that the theory must besomewhat improved in order to match higher precision data: for more details see[389].Fig. 7.10 Histogram of horizontal velocity differences as measured and analyzed by Swinneyet al. [433], and by Bodenschatz et al. [438] in turbulent Couette–Taylor flow experiments(from [328]).